References

XIXA

XIX-A: Clock Separation Before Coordinate Identification: Four Labelled Objects and Five Non-Identifications, anonymous draft supplied in the present manuscript exchange, -A.tex, n.d. Classical comparison only; no quantum certificate is inferred.

XIXB

XIX-B: A Witness Mismatch Between Two Coordinate Cauchy Prescriptions: Unswitched Harmonic Coordinates and Prepared Coordinate Completion, anonymous draft supplied in the present manuscript exchange, -B.tex, n.d. The declared direct first-order mismatch is not a quantum anomaly or a premise of the present proofs.

XIXC

XIX-C: Finite Incidence Registers and the Missing Continuum Evolution: Matching, Records, Promised Tokens, and Scheduled Support, anonymous draft supplied in the present manuscript exchange, -C.tex, n.d. Finite quantum channels and native continuum non-determination remain distinct.

CheungVI

N. Cheung, Relational Einstein–scalar observables at second order: classical descent and a compact-switch obstruction, Landmark VI, version 1, supplied unpublished manuscript, .tex, n.d. Enter Calculus Companion. Relevant documentary section: “Static audit of the proposed quantum certificate.” The quantum finite-renormalization certificate remains RG-open in the supplied record.

CheungEm02E

N. Cheung, Em02-E, version 1, supplied unpublished manuscript, 02-E-v1.tex, n.d. Enter Calculus Companion. Relevant locators: :lapse, :release, and “The quantum input gate and the first contraction target.” Original inflaton-slice rods and the incomplete quantum audit.

CheungXVIIIA

N. Cheung, Landmark XVIII-A: Prepared Relational Observables: Non-Determination, Normalization Compatibility, and Conditional Ultraviolet Matching, version 2, supplied unpublished manuscript, -A-v2.tex, n.d. Enter Calculus Companion. Witness, response, kernel, normalization, fixed-point, and formal-order comparison interfaces.

CheungXVIIIB

N. Cheung, Landmark XVIII-B, version 2, supplied unpublished manuscript, -B-v2.tex, n.d. Enter Calculus Companion. Free massive scalar stress-response benchmark; relevant supplied locator: :spectral. The local benchmark is not a native relational-clock certificate.

CheungVIIIA

N. Cheung, Landmark VIII-A, version 3, supplied unpublished manuscript, -A-v3.tex, n.d. Enter Calculus Companion. Relevant supplied locator: :thm:residual. Record agreement and complete residual-instrument agreement remain distinct.

CheungVIIIB

N. Cheung, Landmark VIII-B, version 3, supplied unpublished manuscript, -B-v3.tex, n.d. Enter Calculus Companion. Finite source, packet, token, and parameter–lapse non-identification interfaces.

CheungVIIIC

N. Cheung, Landmark VIII-C, version 3, supplied unpublished manuscript, -C-v3.tex, n.d. Enter Calculus Companion. Frozen-packet incidence, regular source replacement, complete-output scope, and missing mixed-germ, acquisition, physical-embedding, and dynamics interfaces.

CheungI

N. Cheung, Landmark I, version 2, supplied unpublished manuscript, .tex, n.d. Enter Calculus Companion. Finite measurement semantics and structural characterization; not a field-theoretic instrument construction.

CheungEnter

N. Cheung, “The Enter Calculus: A Linear Quantum Lambda Calculus with an Operational Characterization of Measurement,” Frontiers in Physics 14 (2026), article 1954943. DOI: 10.3389/fphy.2026.1954943. Metadata as supplied in the accepted-article record, accepted 28 September 2026. Finite operational context only; publisher authentication is not claimed by this manuscript.

CheungVIIH

N. Cheung, Landmark VII-H, version 1, supplied unpublished manuscript, -H.tex, n.d. Enter Calculus Companion. Free massless scalar susceptibility, retarded prescription, contact ambiguity, and invariant-test benchmark. Not the massive stress kernel or the inherited characteristic graph.

CheungXVIQ

N. Cheung, XVI-Q, release Q11, supplied unpublished manuscript, -Q.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :o1, :qds, :p6, :classification, :bulk, :insertion, and :package. Scoped one-loop bulk two-point report and its explicit verification and nontransfer qualifications.

CheungXVIP

N. Cheung, XVI-P, version p23, supplied unpublished manuscript, -P.tex, n.d. Enter Calculus Companion. Declared two-point prescription, ghost-orientation correction, external-leg scheme, and separately scoped identity flags.

CheungXVIO

N. Cheung, XVI-O, version o70-sync, supplied unpublished manuscript, -O.tex, n.d. Enter Calculus Companion. Kernel two-point Ward subsector under its own prescription; not the enlarged Q11 prescription or bulk BV restoration.

CheungXVIN

N. Cheung, XVI-N, version r12, supplied unpublished manuscript, -N.tex, n.d. Enter Calculus Companion. Relevant supplied locator: :massless-obstruction. Conditional massless special-family insertion obstruction; spatially compact Route B is not discharged.

CheungXVIH

N. Cheung, Landmark XVI-H: Compact polarized kernel and witness recovery, version 1, supplied unpublished manuscript, -H.tex, n.d. Enter Calculus Companion. Compact kernel and partial witness recovery under stated root inputs; admission and prepared quantum-product boundaries remain distinct.

CheungOai282B

N. Cheung, Oai282-B, version 1, supplied unpublished manuscript, 282-B.tex, n.d. Enter Calculus Companion. Declared homogeneous free-scalar local Ward class, finite coverage, and local/global nontransfer comparisons. Not an OpenAI family verification.

CheungOai069A

N. Cheung, Oai069-A, version 1, supplied unpublished manuscript, 069-A.tex, n.d. Enter Calculus Companion. Finite Ward-defect comparison and finite-monodromy/local-system benchmark; relevant supplied locator: :category. No gravitational or positive-channel dictionary is imported.

Catalogue

OpenAI catalogue and companion scope records, attributed to OpenAI in the supplied documentary record, including Families 271, 282, and 069, record dated 7 October 2026. Enter Calculus Companion. Family 271's reported Lean scope names 271-04 only; VI is not 271-04. Attribution, proof validity, and Lean execution are not independently authenticated here.

CheungXIVH

N. Cheung, Landmark XIV-H: Internal kernel relations on the operator route, version 1, supplied unpublished manuscript, -H.tex, n.d. Relevant supplied locators: :K5exact, :H2, and :release. Sheet-specific internal-amplitude stop.

CheungXIVI

N. Cheung, Landmark XIV-I, version 1, supplied unpublished manuscript, -I.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :I2, :I3, and :release. Internal amplitude construction and remaining joint-map boundary.

CheungXIVJ

N. Cheung, Landmark XIV-J, version 1, supplied unpublished manuscript, -J.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :descent, :null, :reference, :J2, and :noadmission. Supported-sector reference and full-characteristic-map separation.

CheungXVB

N. Cheung, XV-B, version 2, supplied unpublished manuscript, -B.tex, n.d. Enter Calculus Companion. Relative lifting, finite normal jets, and extension interfaces. The inherited complete map and downstream quantum admission are not supplied by those interfaces alone.

CheungIXA

N. Cheung, Landmark IX-A, version 1, supplied unpublished manuscript, -A.tex, n.d. Enter Calculus Companion. Classical sharp-insertion carrier and topology; not a completed quantum deformation.

CheungIXC

N. Cheung, Landmark IX-C, version 1, supplied unpublished manuscript, -C.tex, n.d. Enter Calculus Companion. One-word binary-coherence reductions and necessary tests; not completed binary factorization.

CheungIXFree

N. Cheung, IX-Free, version 1, supplied unpublished manuscript, -Free.tex, n.d. Enter Calculus Companion. Version-qualified partial results and its stated unresolved descent and overlap boundary.

CheungIXFreeTwo

N. Cheung, IX-Free-2, version 1, supplied unpublished manuscript, -Free-2.tex, n.d. Enter Calculus Companion. One relative truncated partial product on its declared tensor domain and coherence of a selected word through ${\hslash }^3$; not time ordering or a complete quantum algebra.

CheungIXD

N. Cheung, Landmark IX-D, version 3, supplied unpublished manuscript, -D-v3.tex, n.d. Enter Calculus Companion. Partial free coherence, time-ordered extension, and normalized retarded maps remain distinct.

CheungIXE

N. Cheung, Landmark IX-E, version 1, supplied unpublished manuscript, -E.tex, n.d. Enter Calculus Companion. Relevant supplied locator: :obstruction. Fixed-domain conditional causal-factorization obstruction; not a universal clock-product obstruction.

CheungXA

N. Cheung, X-A, version 1, supplied unpublished manuscript, -A.tex, n.d. Enter Calculus Companion. Density ramp and its separately stated classical covariance and prerequisite interfaces.

CheungXB

N. Cheung, X-B, version 3, supplied unpublished manuscript, -B-v3.tex, n.d. Enter Calculus Companion. Scalar-only quantum field content with classical metric backgrounds; a quantized-metric branch is separate.

CheungXC

N. Cheung, X-C, version 3, supplied unpublished manuscript, -C-v3.tex, n.d. Enter Calculus Companion. Fixed-width scalar response maps through second coupling order on the declared off-shell linear tests.

CheungXD

N. Cheung, X-D, version 3, supplied unpublished manuscript, -D-v3.tex, n.d. Enter Calculus Companion. Coefficient-test limit at fixed input in its stated quotient topology; not joint sharp quantum admission.

CheungXE

N. Cheung, X-E, version 1, supplied unpublished manuscript, -E.tex, n.d. Enter Calculus Companion. One-tree quantum-metric benchmark and its stated order boundary.

CheungXF

N. Cheung, X-F, version 1, supplied unpublished manuscript, -F.tex, n.d. Enter Calculus Companion. Three-tree background identity through ${\kappa }^2{\hslash }^0$; no loop identity is transferred.

CheungXG

N. Cheung, X-G, version 1, supplied unpublished manuscript, -G.tex, n.d. Enter Calculus Companion. Free graded multiplet, specified source-preserving variational upgrade obstruction, and separate unresolved one-loop target.

BFHPR

R. Brunetti, K. Fredenhagen, T.-P. Hack, N. Pinamonti, and K. Rejzner, “Cosmological perturbation theory and quantum gravity,” Journal of High Energy Physics 08 (2016), 032. DOI: 10.1007/JHEP08(2016)032. arXiv:1605.02573. Relational-observable framework; no native prescription identification is inferred.

Frob

M. B. Fröb, “Gauge-invariant quantum gravitational corrections to correlation functions,” Classical and Quantum Gravity 35 (2018), 055006. DOI: 10.1088/1361-6382/aaa74c. arXiv:1710.00839. Relational quantum-correlator context; not the local stress benchmark or an imported clock certificate.

Hack

T.-P. Hack, “Quantization of the linearised Einstein–Klein–Gordon system on arbitrary backgrounds and the special case of perturbations in inflation,” Classical and Quantum Gravity 31 (2014), 215004. DOI: 10.1088/0264-9381/31/21/215004. arXiv:1403.3957. Separate linearized field and gauge construction on on-shell backgrounds.

BFR

R. Brunetti, K. Fredenhagen, and K. Rejzner, “Quantum gravity from the point of view of locally covariant quantum field theory,” Communications in Mathematical Physics 345 (2016), 741–779. DOI: 10.1007/s00220-016-2676-x. arXiv:1306.1058. Locally covariant perturbative gravity and renormalized BV framework; no ultraviolet-completeness conclusion is imported.

BF

R. Brunetti and K. Fredenhagen, “Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds,” Communications in Mathematical Physics 208 (2000), 623–661. DOI: 10.1007/s002200050004. arXiv:math-ph/9903028. Distributional products and extension framework.

HWlocal

S. Hollands and R. M. Wald, “Local Wick polynomials and time ordered products of quantum fields in curved spacetime,” Communications in Mathematical Physics 223 (2001), 289–326. DOI: 10.1007/s002200100540. arXiv:gr-qc/0103074. Local covariance and normalization ambiguities on the stated field-theoretic domain.

HWexistence

S. Hollands and R. M. Wald, “Existence of local covariant time ordered products of quantum fields in curved spacetime,” Communications in Mathematical Physics 231 (2002), 309–345. DOI: 10.1007/s00220-002-0719-y. arXiv:gr-qc/0111108. Local time-ordered-product construction; not a theorem for an unnamed nonlocal clock kernel.

HWreview

S. Hollands and R. M. Wald, “Quantum fields in curved spacetime,” Physics Reports 574 (2015), 1–35. DOI: 10.1016/j.physrep.2015.02.001. arXiv:1401.2026. States, microlocal spectrum conditions, local composites, and perturbative construction on classical backgrounds.

Dang

N. V. Dang, “The extension of distributions on manifolds, a microlocal approach,” Annales Henri Poincaré 17 (2016), 819–859. arXiv:1412.2808. Extension framework only; no application to an unconstructed inherited characteristic target is asserted.

Watrous

J. Watrous, The Theory of Quantum Information, Cambridge University Press, Cambridge, 2018. DOI: 10.1017/9781316848142. Complete channels, reference systems, trace distance, and diamond-norm conventions.